Finite Group Databasebeta

← Group #72337725

Character table — Group #72337725

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112224444448888881616161616161616161616161632323232323232323232323232323232326464646464646464646464128128128128
order12222222222222222222222444444424444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-11111-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11111-1-111
χ5111111111111111-1-111111-11-1-11111-1-11-1-11111-1-111-1-1-1-11-1-1ii−i−iii−i−ii−ii−i
χ6111111111111111-1-111111-11-1-11111-1-11-1-11111-1-111-1-1-1-11-1-1−i−iii−i−iii−ii−ii
χ7111111111111111-1-111111-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-11-11ii−i−i−i−iiii−i−ii
χ8111111111111111-1-111111-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-11-11−i−iiiii−i−i−iii−i
χ911111111111-1-1-1-111111-1-111111111-1-11-1-111-1-1-1-1-1-11111-1-1111111111-1-1-1-1
χ1011111111111-1-1-1-111111-1-111111111-1-11-1-111-1-1-1-1-1-11111-1-11-1-1-1-1-1-1-1-11111
χ1111111111111-1-1-1-111111-1-11111-1-1-1-111111-1-111-1-111-1-111-1-1-11111-1-1-1-1-1-111
χ1211111111111-1-1-1-111111-1-11111-1-1-1-111111-1-111-1-111-1-111-1-1-1-1-1-1-1111111-1-1
χ1311111111111-1-1-1-1-1-1111-1-1-11-1-111111111111-1-111-1-1-1-1-1-1-11-1ii−i−iii−i−i−ii−ii
χ1411111111111-1-1-1-1-1-1111-1-1-11-1-111111111111-1-111-1-1-1-1-1-1-11-1−i−iii−i−iiii−ii−i
χ1511111111111-1-1-1-1-1-1111-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-111ii−i−i−i−iii−iii−i
χ1611111111111-1-1-1-1-1-1111-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-111−i−iiiii−i−ii−i−ii
χ17222222222220000222-2-2002222222200-200-2-200000022-2-200-2000000000000
χ18222222222220000222-2-2002222-2-2-2-200-20022000000-2-2-2-2002000000000000
χ1922222222222000022-2-2-200-2-22-20000222-2-200-2-20022002-2000000000000000
χ2022222222222000022-2-2-200-2-22-20000-2-2222002200-2-2002-2000000000000000
χ21222222222220000-2-22-2-200-22-2-2222200-200-2-2000000-2-222002000000000000
χ22222222222220000-2-22-2-200-22-2-2-2-2-2-200-20022000000222200-2000000000000
χ23222222222220000-2-2-2-2-2002-2-220000222-2-2002200-2-200-22000000000000000
χ24222222222220000-2-2-2-2-2002-2-220000-2-222200-2-2002200-22000000000000000
χ2522222222222222222-22222-2-22-2000000-2000000220000-22-2-20000000000000
χ26222222222222222-2-2-222222-2-22000000-2000000-2-200002-2-220000000000000
χ2722222222222-2-2-2-222-222-2-2-2-22-2000000-2000000-2-20000-22220000000000000
χ2822222222222-2-2-2-2-2-2-222-2-22-2-22000000-20000002200002-22-20000000000000
χ29444444-4-4-4-440000440000000-400000000000000000000000002-22-200000000
χ30444444-4-4-4-440000440000000-40000000000000000000000000-22-2200000000
χ31444444-4-4-4-440000-4-40000000400000000000000000000000002i−2i−2i2i00000000
χ32444444-4-4-4-440000-4-4000000040000000000000000000000000−2i2i2i−2i00000000
χ3344444-444-4-4-4000000400000-4000000000004i−4i0000000000000000000000000
χ3444444-444-4-4-4000000400000-400000000000−4i4i0000000000000000000000000
χ3544444-444-4-4-4000000-4000004004i4i−4i−4i00000000000000000000000000000000
χ3644444-444-4-4-4000000-400000400−4i−4i4i4i00000000000000000000000000000000
χ3744444-4-4-444-400000000000400-400000000000000000000000000002-22-20000
χ3844444-4-4-444-400000000000400-40000000000000000000000000000-22-220000
χ3944444-4-4-444-400000000000-400400000000000000000000000000002i−2i−2i2i0000
χ4044444-4-4-444-400000000000-40040000000000000000000000000000−2i2i2i−2i0000
χ41444-4-4-40000422-2-24-40002-200002-22-20002-2002-22-2002-200000000000000000
χ42444-4-4-40000422-2-24-40002-20000-22-22000-2200-222-200-2200000000000000000
χ43444-4-4-40000422-2-2-440002-200002-22-2000-22002-2-2200-2200000000000000000
χ44444-4-4-40000422-2-2-440002-20000-22-220002-200-22-22002-200000000000000000
χ45444-4-4-400004-2-2224-4000-2200002-22-2000-2200-22-22002-200000000000000000
χ46444-4-4-400004-2-2224-4000-220000-22-220002-2002-2-2200-2200000000000000000
χ47444-4-4-400004-2-222-44000-2200002-22-20002-200-222-200-2200000000000000000
χ48444-4-4-400004-2-222-44000-220000-22-22000-22002-22-2002-200000000000000000
χ49888-8-880000-80000000000000004i−4i−4i4i00000000000000000000000000000000
χ50888-8-880000-8000000000000000−4i4i4i−4i00000000000000000000000000000000
χ5188-88-80008-800000000000000000000000000000004-40000000000000000000
χ5288-88-80008-80000000000000000000000000000000-440000000000000000000
χ5388-88-8000-88044-4-400000-440000000000000000000000000000000000000000
χ5488-88-8000-880-4-444000004-40000000000000000000000000000000000000000
χ5588-8-8808-800000000000000000000004-4000000000000000000000000000000
χ5688-8-8808-80000000000000000000000-44000000000000000000000000000000
χ5788-8-880-88000444400000-4-40000000000000000000000000000000000000000
χ5888-8-880-88000-4-4-4-400000440000000000000000000000000000000000000000
χ5916-16000000000008-80004-4000000000000000000000000000000000000000000
χ6016-1600000000000-880004-4000000000000000000000000000000000000000000
χ6116-160000000008-800000-44000000000000000000000000000000000000000000
χ6216-16000000000-8800000-44000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).